CHAOTIC VIBRATIONS AND RESONANCES IN A FLEXIBLE-ARM ROBOT

Abstract

Once flexibility is introduced into the arm of the robot, severe problems in the accuracy and stability are likely to occur which make control a critical issue. These problems can successfully be eliminated only if the nonlinear dynamics associated with the flexible–arm is properly accounted for. In this paper we study the behaviour of a two degree of freedom high speed robot with a flexible–arm, having quadratic nonlinearities with natural frequencies defined as ω 1 and ω 2 , at ω 1 ∝ 2ω 2 internal resonance. We perform numerical simulations as well as analytical investigations on a simplified mathematical model of the system, subjected to periodic excitation. The two variable expansion perturbation method is used to show the existence of jump phenomena and ‘saturation’ when both forced resonance and internal resonance occur. Numerical studies indicate the existence of chaotic solutions in the resonance regions. The routes to chaos contain subharmonic bifurcations.